Finite Group Databasebeta

← C127×#13605 #44577278

Subgroups — C127×#13605 #44577278

Order 32512.

344 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 86 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3220C211yesmaximal, characteristic
2C127×#2134C211yesmaximal, characteristic, complemented
3C127×#2127C211yesmaximal, characteristic, complemented
4C127×#1414C212yesmaximal, complemented
5C127×#1406C212yesmaximal, complemented
6#540×C127C411yescharacteristic, complemented
7#535×C127C2211yescharacteristic
8#496×C127C2211yescharacteristic
9#493×C127C411yescharacteristic, complemented
10#490×C127C411yescharacteristic, complemented
11#488×C127C2211yescharacteristic
12#463×C127—21no—
13#459×C127—21no—
14#449×C127—21no—
15#447×C127—21no—
16#433×C127C411yescharacteristic, complemented
17#413×C127—21no—
18C2×#99×C127—21no—
19#355×C127—21no—
20#355×C127C2212yes—
21#354×C127C2212yes—
22#353×C127—21no—
23C2×#41×C127D411yescharacteristic
24C22×D4×C127D411yescharacteristic
25C2×SD16×C127—21no—
26C2×D8×C127—21no—
27C2×D8×C127—21no—
28C2×D8×C127—21no—
29C2×M16×C127—41no—
30#127×C127C2×C411yescharacteristic
31#127×C127C2×C411yescharacteristic, complemented
32#127×C127D411yescharacteristic
33#125×C127C2×C411yescharacteristic, complemented
34#124×C127D411yescharacteristic
35#124×C127C2311yescharacteristic
36#123×C127—41no—
37#121×C127—21no—
38#121×C127—41no—
39#121×C127—41no—
40#120×C127—41no—
41C4×D4×C127—21no—
42#117×C127C2×C411yescharacteristic
43C2×C22⋊C4×C127—41no—
44C4⋊C8×C127—21no—
45#103×C127—21no—
46#102×C127—21no—
47#102×C127—21no—
48#102×C127—21no—
49#101×C127—22no—
50#100×C127—41no—
51#99×C127—22no—
52#99×C127—41no—
53C22⋊C8×C127—21no—
54#97×C127C2×C411yescharacteristic, complemented
55C4×C8×C127C2×C411yescharacteristic, complemented
56C24×C127—21no—
57#41×C127—81no—
58C2×Q8×C127C2×D411yescharacteristic
59C2×D4×C127—21no—
60C2×D4×C127—21no—
61C2×D4×C127—21no—
62C2×D4×C127—41no—
63C2×D4×C127—41no—
64C2×D4×C127—41no—
65C2×D4×C127—41no—
66C2×D4×C127—81no—
67C2×D4×C127C22⋊C411yescharacteristic
68C2×D4×C127C22⋊C411yescharacteristic
69C2×D4×C127C2×D411yescharacteristic
70C22×C4×C127—21no—
71C22×C4×C127—41no—
72C22×C4×C127—81no—
73C22×C4×C127C22⋊C411yescharacteristic
74SD16×C127—81no—
75D8×C127—81no—
76D8×C127—81no—
77D8×C127—81no—
78M16×C127—42no—
79M16×C127—81no—
80C2×C8×C127—21no—
81C2×C8×C127—21no—
82C2×C8×C127—81no—
83C4⋊C4×C127—21no—
84C4⋊C4×C127—21no—
85C4⋊C4×C127—41no—
86C22⋊C4×C127—21no—
87C22⋊C4×C127—41no—
88C22⋊C4×C127—41no—
89C22⋊C4×C127—41no—
90C22⋊C4×C127—41no—
91C22⋊C4×C127—42no—
92C22⋊C4×C127—81no—
93C42×C127C22⋊C411yescharacteristic
94C42×C127C22×C411yescharacteristic
95C23×C127—21no—
96C23×C127—21no—
97C23×C127—21no—
98C23×C127—41no—
99C23×C127—41no—
100C23×C127—41no—
101C23×C127—161no—
102C23×C127#9911yescharacteristic
103Q8×C127—41no—
104D4×C127—41no—
105D4×C127—41no—
106D4×C127—41no—
107D4×C127—41no—
108D4×C127—41no—
109D4×C127—81no—
110D4×C127—81no—
111D4×C127—161no—
112D4×C127—161no—
113D4×C127—161no—
114D4×C127—161no—
115C2×C4×C127—21no—
116C2×C4×C127—21no—
117C2×C4×C127—21no—
118C2×C4×C127—41no—
119C2×C4×C127—41no—
120C2×C4×C127—41no—
121C2×C4×C127—41no—
122C2×C4×C127—82no—
123C2×C4×C127—161no—
124C2×C4×C127—162no—
125C2×C4×C127#9911yescharacteristic
126C2×C4×C127C2×C22⋊C411yescharacteristic
127C8×C127—41no—
128C8×C127—41no—
129C8×C127—82no—
130C22×C127—21no—
131C22×C127—41no—
132C22×C127—41no—
133C22×C127—41no—
134C22×C127—41no—
135C22×C127—81no—
136C22×C127—81no—
137C22×C127—81no—
138C22×C127—81no—
139C22×C127—81no—
140C22×C127—82no—
141C22×C127—81no—
142C22×C127—161no—
143C22×C127C2×#9911yescharacteristic
144C4×C127—21no—
145C4×C127—21no—
146C4×C127—41no—
147C4×C127—41no—
148C4×C127—41no—
149C4×C127—81no—
150C4×C127—162no—
151#13605C12711yesmaximal, characteristic, direct product factor, Sylow
152C2×C127—21no—
153C2×C127—41no—
154C2×C127—81no—
155C2×C127—81no—
156C2×C127—81no—
157C2×C127—161no—
158C2×C127#212711yescharacteristic
159#3220C2×C12711yescharacteristic
160#2134C2×C12711yescharacteristic, complemented
161#2127C2×C12711yescharacteristic, complemented
162#1414C2×C12712yescomplemented
163#1406C2×C12712yescomplemented
164C127#1360511yescharacteristic, direct product factor, Sylow
165#540C4×C12711yescharacteristic, complemented
166#535C22×C12711yescharacteristic
167#496C22×C12711yescharacteristic
168#493C4×C12711yescharacteristic, complemented
169#490C4×C12711yescharacteristic, complemented
170#488C22×C12711yescharacteristic
171#463—21no—
172#459—21no—
173#449—21no—
174#447—21no—
175#433C4×C12711yescharacteristic, complemented
176#413—21no—
177C2×#99—21no—
178#355—21no—
179#355C22×C12712yes—
180#354C22×C12712yes—
181#353—21no—
182C2×#41D4×C12711yescharacteristic
183C22×D4D4×C12711yescharacteristic
184C2×SD16—21no—
185C2×D8—21no—
186C2×D8—21no—
187C2×D8—21no—
188C2×M16—41no—
189#127C2×C4×C12711yescharacteristic
190#127C2×C4×C12711yescharacteristic, complemented
191#127D4×C12711yescharacteristic
192#125C2×C4×C12711yescharacteristic, complemented
193#124D4×C12711yescharacteristic
194#124C23×C12711yescharacteristic
195#123—41no—
196#121—21no—
197#121—41no—
198#121—41no—
199#120—41no—
200C4×D4—21no—
201#117C2×C4×C12711yescharacteristic
202C2×C22⋊C4—41no—
203C4⋊C8—21no—
204#103—21no—
205#102—21no—
206#102—21no—
207#102—21no—
208#101—22no—
209#100—41no—
210#99—22no—
211#99—41no—
212C22⋊C8—21no—
213#97C2×C4×C12711yescharacteristic, complemented
214C4×C8C2×C4×C12711yescharacteristic, complemented
215C24—21no—
216#41—81no—
217C2×Q8C2×D4×C12711yescharacteristic
218C2×D4—21no—
219C2×D4—21no—
220C2×D4—21no—
221C2×D4—41no—
222C2×D4—41no—
223C2×D4—41no—
224C2×D4—41no—
225C2×D4—81no—
226C2×D4C22⋊C4×C12711yescharacteristic
227C2×D4C22⋊C4×C12711yescharacteristic
228C2×D4C2×D4×C12711yescharacteristic
229C22×C4—21no—
230C22×C4—41no—
231C22×C4—81no—
232C22×C4C22⋊C4×C12711yescharacteristic
233SD16—81no—
234D8—81no—
235D8—81no—
236D8—81no—
237M16—42no—
238M16—81no—
239C2×C8—21no—
240C2×C8—21no—
241C2×C8—81no—
242C4⋊C4—21no—
243C4⋊C4—21no—
244C4⋊C4—41no—
245C22⋊C4—21no—
246C22⋊C4—41no—
247C22⋊C4—41no—
248C22⋊C4—41no—
249C22⋊C4—41no—
250C22⋊C4—42no—
251C22⋊C4—81no—
252C42C22⋊C4×C12711yescharacteristic
253C42C22×C4×C12711yescharacteristic
254C23—21no—
255C23—21no—
256C23—21no—
257C23—41no—
258C23—41no—
259C23—41no—
260C23—161no—
261C23#99×C12711yescharacteristic
262Q8—41no—
263D4—41no—
264D4—41no—
265D4—41no—
266D4—41no—
267D4—41no—
268D4—81no—
269D4—81no—
270D4—161no—
271D4—161no—
272D4—161no—
273D4—161no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—82no—
282C2×C4—161no—
283C2×C4—162no—
284C2×C4#99×C12711yescharacteristic
285C2×C4C2×C22⋊C4×C12711yescharacteristic
286C8—41no—
287C8—41no—
288C8—82no—
289C22—21no—
290C22—41no—
291C22—41no—
292C22—41no—
293C22—41no—
294C22—81no—
295C22—81no—
296C22—81no—
297C22—81no—
298C22—81no—
299C22—82no—
300C22—81no—
301C22—161no—
302C22C2×#99×C12711yescharacteristic
303C4—21no—
304C4—21no—
305C4—41no—
306C4—41no—
307C4—41no—
308C4—81no—
309C4—162no—
310C2—21no—
311C2—41no—
312C2—81no—
313C2—81no—
314C2—81no—
315C2—161no—
316C2C127×#212711yescharacteristic
subgroupG/H
center, socleC2×C127#2127
commutatorC42C22×C4×C127
Frattini, cosocle#124C23×C127
prime radicalC127×#3220C2
LCSG ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C127 ◁ C22×C127 ◁ C22×C4×C127 ◁ #535×C127 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C127×#2134C2semidirect
3. C127×#2127C2semidirect
4. C127×#1414C2semidirect
5. C127×#1406C2semidirect
6. #540×C127C4semidirect
9. #493×C127C4semidirect
10. #490×C127C4semidirect
16. #433×C127C4semidirect
31. #127×C127C2×C4semidirect
33. #125×C127C2×C4semidirect
54. #97×C127C2×C4semidirect
55. C4×C8×C127C2×C4semidirect
151. #13605C127direct (N × H)
160. #2134C2×C127semidirect
161. #2127C2×C127semidirect
162. #1414C2×C127semidirect
163. #1406C2×C127semidirect
164. C127#13605direct (N × H)
165. #540C4×C127semidirect
168. #493C4×C127semidirect
169. #490C4×C127semidirect
175. #433C4×C127semidirect
190. #127C2×C4×C127semidirect
192. #125C2×C4×C127semidirect
213. #97C2×C4×C127semidirect
214. C4×C8C2×C4×C127semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C127×#32202
C127×#21342
C127×#21272
C127×#14142
C127×#14062
#13605127